An improved algorithm for in situ adaptive tabulation

In situ adaptive tabulation (ISAT) is a proven storage/retrieval method which efficiently provides accurate approximations to high-dimensional functions which are computationally expensive to evaluate. Previous applications of ISAT to computations of turbulent combustion have resulted in speed-ups of up to a thousand. In this paper, improvements to the original ISAT algorithm are described and demonstrated using two test problems. The principal improvements are in the table-searching strategies and the addition of an error checking and correction algorithm. Compared to an earlier version of ISAT, reductions in CPU time and storage requirements by factors of 2 and 5, respectively, are observed for the most challenging, 54-dimensional test problem.

[1]  Stephen B. Pope,et al.  PDF calculations of major and minor species in a turbulent piloted jet flame , 1998 .

[2]  A. Armaou,et al.  Multiscale optimization using hybrid PDE/kMC process systems with application to thin film growth , 2005 .

[3]  N. H. Kolhapure.  PDF Simulations of Ethylene Decomposition in Tubular LDPE Reactors (Journal Review) , 2005 .

[4]  Zhuyin Ren,et al.  An investigation of the performance of turbulent mixing models , 2004 .

[5]  Habib N. Najm,et al.  Modeling unsteady reacting flow with operator splitting and ISAT , 2006 .

[6]  Sanjay M. Correa,et al.  Turbulence-chemistry interactions in the intermediate regime of premixed combustion☆ , 1993 .

[7]  Rodney O. Fox,et al.  Computational Fluid Dynamics Simulation of Chemical Reactors: Application of in Situ Adaptive Tabulation to Methane Thermochlorination Chemistry , 1999 .

[8]  Robert L. Gordon,et al.  A numerical study of auto-ignition in turbulent lifted flames issuing into a vitiated co-flow , 2007 .

[9]  S. Pope.  The probability approach to the modelling of turbulent reacting flows , 1976 .

[10]  Thomas F. Edgar,et al.  Approximate nonlinear model predictive control with in situ adaptive tabulation , 2008, Comput. Chem. Eng..

[11]  Assaad R. Masri,et al.  Artificial neural network implementation of chemistry with pdf simulation of H2/CO2 flames , 1996 .

[12]  Rodney O. Fox,et al.  Multi-environment probability density function method for modelling turbulent combustion using realistic chemical kinetics , 2007 .

[13]  Stephen B. Pope,et al.  Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation , 1997 .

[14]  Paul E. Plassmann,et al.  A Scientific On-line Database for Efficient Function Approximation , 2003, ICCSA.

[15]  Sandip Mazumder Mem.  Modeling Full-Scale Monolithic Catalytic Converters: Challenges and Possible Solutions , 2007 .

[16]  Norberto Fueyo,et al.  An economical strategy for storage of chemical kinetics: Fitting in situ adaptive tabulation with artificial neural networks , 2000 .

[17]  Paul E. Plassmann,et al.  Parallel Heuristics for an On-Line Scientific Database for Efficient Function Approximation , 2004, PARA.

[18]  Tamás Turányi,et al.  Parameterization of Reaction Mechanisms Using Orthonormal Polynomials , 1994, Comput. Chem..

[19]  Sandip Mazumder,et al.  Adaptation of the in situ adaptive tabulation (ISAT) procedure for efficient computation of surface reactions , 2005, Comput. Chem. Eng..

[20]  B. Fan,et al.  Acceleration of chemistry computations in two-dimensional detonation induced by shock focusing using reduced ISAT , 2007 .

[21]  S. Pope,et al.  The effect of mixing models in PDF calculations of piloted jet flames , 2007 .

[22]  Johannes Gehrke,et al.  High-Speed Function Approximation , 2007, Seventh IEEE International Conference on Data Mining (ICDM 2007).

[23]  Habib N. Najm,et al.  Operator-splitting with ISAT to model reacting flow with detailed chemistry , 2006 .

[24]  J.-Y. Chen.  ANALYSIS OF IN SITU ADAPTIVE TABULATION PERFORMANCE FOR COMBUSTION CHEMISTRY AND IMPROVEMENT WITH A MODIFIED SEARCH ALGORITHM , 2004 .

[25]  S. James,et al.  Large eddy simulations of turbulent flames using the filtered density function model , 2007 .

[26]  Richard D. Hornung,et al.  Embedded polycrystal plasticity and adaptive sampling , 2008 .

[27]  S. Pope.  PDF methods for turbulent reactive flows , 1985 .

[28]  Norberto Fueyo,et al.  Modelling the Temporal Evolution of a Reduced Combustion Chemical System With an Artificial Neural Network , 1998 .

[29]  Bart Merci,et al.  Impact of Turbulent Flow and Mean Mixture Fraction Results on Mixing Model Behavior in Transported Scalar PDF Simulations of Turbulent Non-premixed Bluff Body Flames , 2007 .

[30]  H. Rabitz,et al.  General foundations of high‐dimensional model representations , 1999 .

[31]  Stephen B. Pope,et al.  An investigation of the accuracy of manifold methods and splitting schemes in the computational implementation of combustion chemistry , 1998 .

[32]  Sanjay M. Correa,et al.  Models for high-intensity turbulent combustion , 1994 .

[33]  Johannes Gehrke,et al.  Indexing for function approximation , 2006, VLDB.

[34]  Stephen B. Pope,et al.  A Systematic Investigation of In Situ Adaptive Tabulation for Combustion Chemistry , 2007 .

[35]  Jing Chen,et al.  Stochastic modeling of partially stirred reactors , 1997 .

[36]  Michael Frenklach,et al.  PRISM: piecewise reusable implementation of solution mapping. An economical strategy for chemical kinetics , 1998 .

[37]  R. E. Rudd,et al.  Generalized in situ adaptive tabulation for constitutive model evaluation in plasticity , 2005 .

[38]  W. E. Stewart,et al.  Sensitivity analysis of initial value problems with mixed odes and algebraic equations , 1985 .

[39]  Stephen B. Pope,et al.  The performance of in situ adaptive tabulation in computations of turbulent flames , 2005 .

[40]  Stephen B. Pope,et al.  An integrated PDF/neural network approach for simulating turbulent reacting systems , 1996 .